Quasi-Monte Carlo methods and pseudo-random numbers

By H. Niederreiter. 1978

CONTENTS

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Quantum random number generators (2016, methodology): “A particularly important area is Monte Carlo and Quasi-Monte Carlo methods (Gentle, 2009; Metropolis and Ulam, 1949; Niederreiter, 1978) in which we can find the solution to a complex problem by averaging many random instances.”
Using Random Quasi-Monte-Carlo Within Particle Filters, With Application to Financial Time Series (2005, methodology): “For further details see Niederreiter (1978), Niederreiter (1992) and Owen (1998).”
Design of computer experiments: A review (2017, methodology): “According to the Koksma-Hlawka inequality [80, 118], the approximation error is upper-bounded by the star discrepancy discussed earlier (Eq.”
Walsh Spaces Containing Smooth Functions and Quasi-Monte Carlo Rules of Arbitrary High Order (2008, unknown): “…for the following two cases: 1. for suﬃciently smooth periodic functions arbitrary high convergence can be achieved using Kronecker sequences [18, Theorem 5.3] or a modiﬁcation of digital nets recently introduced in [2]; 2. a convergence of O ( N − 1 (log N ) s − 1 ) can be achieved for…”
Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration (2010, background): “These early results are well summarised in [61, 112, 128, 169, 175], where much more information on the history and earlier discoveries can be found.”
Zaremba’s conjecture (2011, background): “;2;:::;Ag= N: Zaremba’s conjecture has important applications to numerical integration and pseudorandom number generation, producing collections of points of optimal discrepancy; see e.g. the surveys [Nie78] and [Kon13]. Our main result is the following Theorem 1.2. Almost every positive integer is ”
Acta Numerica: High dimensional integration - the Quasi-Monte Carlo way (2014, unknown): “Kronecker sequences were studied by Niederreiter (1978).”
Least squares polynomial chaos expansion: A review of sampling strategies (2017, methodology): “…convergence rate of standard MC technique, especially for high-dimensional integrations in ﬁnance applications [120], researchers have proposed a deterministic version of the MC sampling method based on the low-discrepancy sequences [26] known as quasi-Monte Carlo (QMC) technique [89, 14, 8, 79].”
An Intercomparison of Sampling Methods for Uncertainty Quantification of Environmental Dynamic Models (2015, unknown): “In Sobol' (1967), both of Halton and Sobol’ sequence was unified as LP-sequence (see definition 3.8 in Niederreiter, 1978).”
An Improvement to Zaremba’s Conjecture (2013, background): “ of Proposition3.438 References 44 1. Introduction 1.1. History of Zaremba’s Conjecture. Zaremba’s conjecture has been closely related to numerical integration and pseudorandom number generation, see [Nie78] and [Kon13]. Several new assertions were made since Zaremba’s conjecture was proposed in 197”
On the average value of divisor sums in arithmetic progressions (2005, methodology): “Finally, we can apply the results of [16, 17, 18] to the function ψ(n) = e (ag/m), where (ag,m) = 1 and g > 1 is of prime multiplicative order p modulo m.”
On the statistical properties of Diffie-Hellman distributions (2000, background): “It follows from Lemma 2 of [21] or Theorem 8.2 of [ 28 ] that the last sum does not exceed p1/2.”